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Finite-dimensional approximations of distributed RC networks

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Spectral properties of ladder and spatial electrical networks are considered. Dynamic properties of the networks are characterised by eigenvalues of the Jacobi cyclic state matrix. The effective formulas for eigenvalues of appropriate uniform systems are given. Numerical calculations were made using MATLAB.
Rocznik
Strony
263--269
Opis fizyczny
Bibliogr. 39 poz., rys.
Twórcy
autor
  • AGH University of Science and Technology, Faculty of Electrical Engineering, Automatics, Computer Science and Biomedical Engineering, Department of Automatics and Biomedical Engineering, 30/B1 A. Mickiewicza Ave., 30–059 Krakow, Poland
Bibliografia
  • [1] M. Janicki, J. Banaszczyk, B. Vermeersch, G. De Mey, and A. Napieralski, “Generation of reduced thermal models of electronic systems from time constant spectra of transient temperature responses”, Microelectronics Reliability 51 (8), 1351–1355 (2011).
  • [2] J. Roszkiewicz, Distributed RC Systems, WKiŁ, Warszawa, 1972, (in Polish).
  • [3] A. Auer, Analog Modeling of Distributed Processes, MM PWN, Warszawa, 1976, (in Polish).
  • [4] A.G. Butkowski, Optimal Control Systems with Distributed Parameters, Moskwa, 1965, (in Russian).
  • [5] K. Deng, P. Barooah, P.G. Mehta, and S.P. Meyn, “Building thermal model reduction via aggregation of states”, American Control Conf. 1, 5118–5123 (2010).
  • [6] E. Kącki, Partial Differential Equations in Physics and Engineering. WNT, Warszawa, 1992, (in Polish).
  • [7] R. Marshall, “Modeling DNA/RNA strings using resistor—capacitor (rc) ladder networks”, Computer J. 53 (6), 644–660 (2009).
  • [8] S.G. Michlin and C.L. Smolicki, Approximate Methods of Solving Differential and Integral Equations, PWN, Warszawa, 1970, (in Polish).
  • [9] T. Cholewicki, An Electrical Long Lines and Nonuniform Ladder Networks, PWN, Warszawa, 1974, (in Polish).
  • [10] W. Mitkowski, “Approximation of an infinite line by a ladder network”, Archives Electrotechnics 25 (4), 943–953 (1976), (in Polish).
  • [11] W. Mitkowski, “Uniform spatial networks RC”, Archives Electrotechnics 22 (2), 397–405 (1973), (in Polish).
  • [12] W. Mitkowski, “Uniform spatial networks RC (RL and GC) type”, Proc. SSCT 74 2, 73–76 (1974).
  • [13] R. Bellman, Introduction to Matrix Analysis, McGraw-Hill, New York, 1960.
  • [14] F.R. Gantmaher, Theory of Matrix, 4 ed., Nauka, Moskwa, 1988, (in Russian).
  • [15] W.P. Ilin and Yu.I. Kuznyetsow, Tridiagonal Matrices and Their Applications, Nauka, Moskwa, 1985, (in Russian).
  • [16] P. Lancaster, Theory of Matrix, Academic Press, New York, 1969.
  • [17] A. Turowicz, Theory of Matrix, 6 ed., AGH, Kraków, 2005, (in Polish).
  • [18] Z. Bubnicki, “Input impedance and transfer function of a ladder network”, IEEE Trans. on Circuit Theory 10, 286–287 (1963).
  • [19] W. Mitkowski, Synthesis of RC-ladder network, Bull. Pol. Ac.: Tech. 42, 33–37 (1994).
  • [20] M.N.S. Swamy, “Network properties of a pair of generalized polynomials”, Circuits and Systems, IEEE Proc. 1, 114–117 (1998).
  • [21] G. Sarwas, “Modelling and control of systems with ultracapacitors using fractional order calculus”, Doctoral Thesis, pp. 1–102, Warsaw University of Technology, Faculty of Electrical Engineering, Warszawa, 2012.
  • [22] R. Caponetto, G. Dongola, L. Fortuna, and I. Petr´aˇs, Fractional Order Systems: Modeling and Control Applications, World Scientific, London, 2010.
  • [23] A. Dzielinski, G. Sarwas, and D. Sierociuk “Comparison and validation of integer and fractional order ultracapacitor models”, Advances in Difference Equations 1, 11–23, (2011).
  • [24] W. Mitkowski and P. Skruch, “Fractional-order models of the supercapacitors in the form of RC ladder networks”, Bull. Pol. Ac.: Tech. 61 (3), 581–587 (2013).
  • [25] W. Mitkowski, “Dynamic properties of chain systems with applications to biological models”, Archives of Control Sciences 9 (XLV), 123–131 (1999).
  • [26] M. Alioto, G. Palumbo, and M. Poli, “An approach to energy consumption modeling in RC ladder circuits”, in Integrated Circuit Design. Power and Timing Modeling, Optimization and Simulation Lecture Notes in Computer Science, vol. 2451, pp. 239–246, Springer, Berlin, 2002.
  • [27] M. Alioto, G. Palumbo, and M. Poli, “Evaluation of energy consumption in RC ladder circuits driven by a ramp input”, IEEE Trans. on Very Large Scale Integration (VLSI) Systems 12 (10), 1094–1107 (2004).
  • [28] J. Baranowski and W. Mitkowski, “Semi-analytical methods for optimal energy transfer in RC ladder networks”, Przegląd Elektrotechniczny (Electrical Review) 88 (9a), 250–254 (2012).
  • [29] W. Mitkowski, “Remarks about energy transfer in an RC ladder network”, Int. J. Appl. Math. Comput. Sci. 13 (2), 193–198 (2003).
  • [30] J. Cheng and T. Berger, “On minimal eigenvalues of a class of tridiagonal matrices”, IEEE Trans. on Information Theory 55 (11), 5024–5031 (2009).
  • [31] W. Mitkowski, “Remarks on stability of positive linear systems”, Control and Cybernetics 29 (1), 295–304 (2000).
  • [32] J. Klamka, Controllability of Dynamic Systems, PWN, Warszawa, 1990, (in Polish).
  • [33] J. Klamka, “Controllability of Dynamical Systems”, Matematyka Stosowana 9, 57-75 (2008).
  • [34] J. Klamka, “Constrained approximate controllability”, IEEE Trans. on Automatic Control 45, 1745-1749 (2000).
  • [35] A. Djouambi, A. Charef, and A. Voda Besanc¸on, “Optimal approximation, simulation and analog realization of the fundamental fractional order transfer function”, Int. J. Appl. Math. Comput. Sci. 17 (4), 455–462 (2007).
  • [36] T. Kaczorek, Selected Problems in Fractional Systems Theory, Springer-Verlag, Berlin, 2011.
  • [37] T. Kaczorek and Ł. Sajewski, Realization Problem for Positive and Fractional Systems, Printing House of Bialystok University of Technology, Białystok, 2013.
  • [38] J. Klamka, “Controllability and minimum energy control problem of fractional discretetime systems”, in New Trends in Nanotechology and Fractional Calculus, eds. D. Baleanu, Z.B. Guvenc and J.A. Tenreiro Machado, pp.503–509, Springer-Verlag, New York, 2010.
  • [39] J. Klamka, “Local controllability of fractional discrete-time nonlinear systems with delay in control”, in: Advances in Control Theory and Automation, eds. M. Busłowicz and K. Malinowski, pp. 25–34, Printing House of Białystok University of Technology, Białystok, 2012.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a86c5ecd-4d4d-42bf-b063-4df68fbdbd92
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